(10) Let (X, B) be a measurable space and {µn} a sequence of measures with the property that for every E E B, H(E) < Hn+1(E'), n = 1,2,.... Let 4(E) lim (E). Show that (X, B, u) is a measure space.
(10) Let (X, B) be a measurable space and {µn} a sequence of measures with the property that for every E E B, H(E) < Hn+1(E'), n = 1,2,.... Let 4(E) lim (E). Show that (X, B, u) is a measure space.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Let (X, B) be a measurable space and {μn} a sequence of
measures with the property that for every E ∈ B,
μn(E) ≤ μn+1(E), n = 1, 2,... .
Let μ(E) = limn→∞ μn(E). Show that (X, B, μ) is a measure
space.
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